Details

Time bar (total: 10.5s)

sample77.0ms

Algorithm
intervals
Results
16.0ms177×body80valid
15.0ms37×body2560valid
10.0ms31×body1280valid
6.0ms92×body80nan
4.0ms16×body640valid
2.0ms5×body5120valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify55.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
01217
12117
24116
37516
48716
59516
done9516

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b
(- (* b b) (* (* 3.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
35.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
48.0ms
(- (* b b) (* (* 3.0 a) c))
67.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify938.0ms

Counts
82 → 82
Iterations

Useful iterations: done (936.0ms)

IterNodesCost
01541565
14011463
213281247
done50001237

prune235.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize17.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.6b
(/ (/ (+ (* b (- b b)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.5b
(/ (+ (* b (- b b)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
27.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
49.0ms
(/ (/ (+ (* b (- b b)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
33.0ms
(/ (+ (* b (- b b)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
6.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series439.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
124.0ms
(/ (/ (+ (* b (- b b)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
165.0ms
(/ (+ (* b (- b b)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
74.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.1s

Counts
166 → 166
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02625855
16715308
223454562
done50004560

prune460.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

localize17.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.6b
(/ (/ (+ (* 3.0 (* a c)) 0) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
8.5b
(/ (+ (* 3.0 (* a c)) 0) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
27.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
30×add-sqr-sqrt
29×*-un-lft-identity
25×add-cube-cbrt
18×add-exp-log add-cbrt-cube
12×associate-/l*
10×associate-*r/ associate-/r/
8×add-log-exp
7×cbrt-undiv flip3-- div-exp flip--
6×div-inv
5×pow1
4×associate-/r* sqrt-prod
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 114
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
29.0ms
(/ (/ (+ (* 3.0 (* a c)) 0) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
29.0ms
(/ (+ (* 3.0 (* a c)) 0) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series486.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
152.0ms
(/ (/ (+ (* 3.0 (* a c)) 0) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
183.0ms
(/ (+ (* 3.0 (* a c)) 0) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
72.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts
126 → 126
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02533830
16393341
230143013
done50003011

prune409.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.9b

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.6b
(/ (/ (/ (* 3.0 (* a c)) 3.0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
8.5b
(/ (/ (* 3.0 (* a c)) 3.0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
27.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
518×times-frac
322×add-sqr-sqrt
321×*-un-lft-identity
173×add-cube-cbrt
74×distribute-lft-out-- difference-of-squares
62×associate-/l*
42×div-inv
40×sqrt-prod
38×add-exp-log add-cbrt-cube
37×distribute-rgt-neg-in
19×cbrt-undiv div-exp
10×associate-/r* associate-/r/
8×add-log-exp
7×flip3-- flip--
6×prod-exp cbrt-unprod
5×pow1
2×frac-2neg sqrt-div diff-log clear-num associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 361
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
51.0ms
(/ (/ (/ (* 3.0 (* a c)) 3.0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
26.0ms
(/ (/ (* 3.0 (* a c)) 3.0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series493.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
155.0ms
(/ (/ (/ (* 3.0 (* a c)) 3.0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
183.0ms
(/ (/ (* 3.0 (* a c)) 3.0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
74.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.1s

Counts
373 → 373
Iterations

Useful iterations: done (1.1s)

IterNodesCost
049913434
1126912859
done500112729

prune910.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 3.9b

regimes461.0ms

Accuracy

87.8% (3.4b remaining)

Error of 8.9b against oracle of 5.5b and baseline of 33.2b

bsearch139.0ms

Steps
ItersRangePoint
3
9.199102238044756e-11
1.1303867620315504e-10
1.0646128438355895e-10
9
3.46724365866438e-191
2.756247811253959e-183
2.225788739342962e-183
8
-1.8857580818171304e+129
-3.0985365288236678e+125
-4.2673012400424376e+128

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03870
14970
done4970

end0.0ms

sample1.1s

Algorithm
intervals
Results
247.0ms1046×body2560valid
228.0ms5917×body80valid
154.0ms862×body1280valid
110.0ms2864×body80nan
64.0ms451×body640valid
31.0ms113×body5120valid
25.0ms230×body320valid
7.0ms101×body160valid